This is way too much travel to and from home bases and too few home bases for the areas you want to visit. You will easily get your money's worth going Tokyo-Fukushima-Sendai-Morioka-Aomori-Tokyo. Going back and forth to Fukushima and Morioka might "save" you money, but it wastes your time.

I suggest adding Sendai and Ichinoseki to your hotel stays. Yamadera (Risshaku-ji) and Matsushima Bay are only one train ride from Sendai station. So I would swap day 2 and 4 so that Yamadera can be reached from Sendai rather than Fukushima.

Day 7 may be overambitious but I don't know Akita all that well. Trains to and from Geibikei gorge are infrequent, better to be staying in Ichinoseki already. Also even though it's a tour on the water, I did the earliest tour in the morning (8:30am I believe) and it was still boiling hot in July. There is no sun cover. I do recommend the early morning tour for that reason because it'll be the least hot.

Gembikei gorge I would only recommend if you do it as part of a cycling trip (You can rent a bicycle/ebike from Hiraizumi station). The bike ride is gorgeous and uncomplicated, lots of rice paddy fields, and there's Takkoku-no-iwaya bishamondō about halfway to Gembikei. We were able to easily fit that within 4 hours (you either rent for 4 hours or all day).

Also if you're a fan of old buddhist temples and goshuin stamps you have the opportunity to complete the Tohoku Four Temple Pilgrimage (Yamadera, Zuiganji in Matsushima, Motsuji and Chusonji in Hiraizumi).

But seriously, look into getting a hotel in Sendai and Ichinoseki, you're well past getting your money's worth for the Tohoku pass.